H_∞ controller design for affine fuzzy systems based on piecewise Lyapunov functions in finite-frequency domain

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• 作者：Huimin Wang^a ; ^{wanghuimin_neu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Guang-Hong Yang^a ; ^b ; ^{yangguanghong@ise.neu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Affine fuzzy models ; Finite frequency ; Piecewise Lyapunov function ; Linear matrix inequalities (LMIs)
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：290
• 期：Complete
• 页码：22-38
• 全文大小：405 K

文摘

This paper studies the problem of state feedback controller design for a class of nonlinear systems described by continuous-time affine fuzzy models. Based on a piecewise continuous Lyapunov function combined with S-procedure and some matrix decoupling techniques, a novel control law is derived in the formulation of linear matrix inequalities (LMIs) in finite-frequency domain. First, a so-called finite-frequency H_∞$H_{\infty }$ performance index is defined, which extends the standard H_∞$H_{\infty }$ performance. Then, a sufficient condition is derived such that the fuzzy closed-loop system satisfies a finite-frequency H_∞$H_{\infty }$ performance. By introducing the S-procedure and adding slack variables, piecewise controllers are designed to deal with disturbances in the low-, middle-, and high-frequency domain, respectively. The proposed piecewise controller design method can get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. Finally, two examples are given to illustrate the effectiveness and superiority of the new results.